While the 555 oscillator IC is a very versatile device, it can also be quite tricky and solutions are not always obvious. Such is the case with this edge-triggered 555 monostable circuit. By differentiating the trigger signal, the monostable multivibrator times out normally regardless of the trigger signal length.
More than a capacitor
The classic differentiator circuit consists of a capacitor and resistor. In this way, the positive change in the trigger signal is coupled to the 555 via C2. When the trigger signal eventually resets, D2 is required to prevent the change in voltage from creating a substantial negative spike. While a negative transient of this nature is unlikely to cause damage, it could well cause temporary IC malfunction.
R-C timing circuit
C1 and the series resistance of R1 to R3 affect the timeout function. Circuit values may be selected per application requirements. This part of the circuit is fairly typical.
Driving the relay
The 555 output is virtually always in the incorrect polarity. However in this case, the relay is working against the positive 12V rail so its operation is effectively inverted. Note the clamp diode that is across the relay coil.
About the test circuit
To generate a trigger signal, I used a miniature pushbutton that works against Vcc. The relay contacts are connected to drive an LED.